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Math Help - trigonometry problems

  1. #1
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    trigonometry problems

    there are three questions.


    1.Given that cos Ѳ = (1/2) and 270 < Ѳ < 360 , without using a calculator find the value of
    (cos Ѳ – sin Ѳ)/(tan Ѳ+ sin Ѳ). Leave your answer as single fraction. Remain the surds as surds if there are surds in your answer.

    2.Given that cos A = (1/2) and that cos A and sin A have the same sign, find the value of sin (–A) and of tan A.

    3.Given that tan A = –(5/12) and that tan A and cos A have opposite signs, find the value of cos A and of cos [(∏/2)–A].
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by wintersoltice View Post
    there are three questions.


    1.Given that cos Ѳ = (1/2) and 270 < Ѳ < 360 , without using a calculator find the value of
    (cos Ѳ sin Ѳ)/(tan Ѳ+ sin Ѳ). Leave your answer as single fraction. Remain the surds as surds if there are surds in your answer.
    Maybe this'll help!
    Attached Thumbnails Attached Thumbnails trigonometry problems-theta.bmp  
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by wintersoltice View Post
    there are three questions.


    1.Given that cos Ѳ = (1/2) and 270 < Ѳ < 360 , without using a calculator find the value of
    (cos Ѳ sin Ѳ)/(tan Ѳ+ sin Ѳ). Leave your answer as single fraction. Remain the surds as surds if there are surds in your answer.

    2.Given that cos A = (1/2) and that cos A and sin A have the same sign, find the value of sin (A) and of tan A.

    3.Given that tan A = (5/12) and that tan A and cos A have opposite signs, find the value of cos A and of cos [(∏/2)A].
    alternatively, recall some useful identities:

    \sin^2 x + \cos^2 x = 1

    \tan x = \frac {\sin x}{\cos x}

    you know what quadrants these angles will be in, if not, see what masters and kalagota did. couple these identities with the ones kalagota gave for problems 2 and 3, and it is straight arithmetic from there.
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  4. #4
    A riddle wrapped in an enigma
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    2.Given that cos A = (1/2) and that cos A and sin A have the same sign, find the value of sin (A) and of tan A.

    Sin and Cos are both positive in Quadrant I and both negative in Quadrant III.

    So if Cos A = 1/2, then the angle must be a QI angle.
    Attached Thumbnails Attached Thumbnails trigonometry problems-angle-.bmp  
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